This is a common in Reformed Theology.
There's much to talk about the 3 offices and functions. As for offices, it is well known that other than Melchizedek, who is mentioned only 3 times in the Bible (Genesis, Psalm 110:4, Hebrews 7), there can be no children of God that hold both the office of priesthood and king, until the Messiah: Zechariah 6:13 "...And there shall be a priest on his throne, and the counsel of peace shall be between them both" ESV
However, the office of Prophet is unique. It is not restricted from holding either of the two other offices simultaneously.
＃祭司、君王兩職不兼任，上帝如何藉先知撒迦利亞預告彌賽亞在兩職之間籌定和平❓（希伯來書要理問答 第872問） [kpVw9NGhRE4]
To explore biblical rule against holding both priestly and kingship office, there are plenty of laws restriction priesthood outside of the heir of Aaron: Numbers 3:10, 3:38, and 16:40. And Genesis 49:10 prophesied (not a command) that the ruler's staff would not depart from Judah.
The exercising of both such offices are always met with serious rebuke and consequences:
(From Google AI) King Saul offers a sacrifice:
- 1 Samuel 13:12–14 recounts how King Saul, in his impatience, offered a burnt offering himself instead of waiting for the priest Samuel.
- Saul's Punishment: Samuel rebuked Saul, telling him, "You have done a foolish thing... The Lord would have established your kingdom over Israel for all time, but now your kingdom will not endure" (1 Samuel 13:13–14, NIV). His kingdom was taken from him as a consequence.
King Uzziah burns incense in the temple:
- 2 Chronicles 26:16–21 details how King Uzziah, after becoming powerful, became arrogant and entered the temple to burn incense, a duty reserved for the priests.
- Uzziah's Punishment: Eighty courageous priests, led by the high priest Azariah, confronted the king. While Uzziah raged at them, leprosy broke out on his forehead. He was driven from the temple and lived as a leper until his death.